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United States flag law does not specify the proportions of the flag. The proportions of 10:19, so often quoted, are the product of an executive order of the president, and are actually binding only in certain military uses. The United States
government buys and uses flags in several other proportions (2:3, 3:5, 5:8) for numerous civilian and military applications. Private citizens are free to use their own judgment.
John Ayer, 6 February 1999
The proportions of the U.S. flag are almost the same as those of British naval ensigns in the 1770's. They attained this rather strange proportion because the table of sizes, issued by Samuel Pepys, Secretary of the Admiralty in 1687, laid down that flags should be made a yard long for every breadth of bewper (bunting) used in their construction. At the time bewper was 22 inches wide, so 22 x 36 gave the excellent proportions of 11:18, which are the whole numbers, near the "Golden Ratio" of 1 : 1.618. Later, bewper was woven in successively smaller widths, but the flags were still made-up in yard lengths. Consequently the proportions changed from 11:18 in 1687 to 1:2 in 1837. In the 1770's bewper was 19 inches wide, so the flags then had the proportions 19:36 or 9.5:18; very close to 10:19.
Note. The flags were actually made-up in half-breadths and half-yards, but the explanation is simpler if given in whole units and doesn't affect the proportions.
David Prothero, 30 January 1999
The source for U.S. flag proportions is actually Executive Order 10834
Joe McMillan, 16 July 1999
For those interested in other service practices, the Air Force follows the Army practice; the larger national color is used only with the ceremonial flag of the Air Force itself; national colors of other commands and units are the smaller size. Marine and Navy units use only the larger size.
The origin of the different sizes may also be of historical interest. The 36x48" dimensions were originally those of the standard (vs. color) used by mounted units--cavalry and later field artillery and mounted engineers. When the Army developed aviation units, they were also considered "mounted" [presumably accounting for the modern Air Force's use of the 36x48" flag]. When the tank came along, armored units also seemed "mounted." Then came mechanized infantry--"mounted" too. All these units carried standards rather than colors. Eventually, there came to be fewer and fewer "foot" units and the 52x66" flag was abandoned as an organizational color except for the 1st Bn 3rd Infantry (now simply referred to as the 3rd Infantry without a battalion designation--the regiment is divided directly into companies) and the U.S. Corps of Cadets. At the same time, the Army dropped the use of the term "standard," even for regiments still officially designated as cavalry.
BTW, the Marines preserve the distinction between "color" and "standard," even though both refer to the same physical flag. When it's carried on foot it's a color; when it's mounted on a vehicle, it's a standard.
Joe McMillan, 17 July 1999
Three items I found at the Navy Department Library last week may be of interest to historians of the U.S. flag:
I posted a message on dimensions of S&S used by the U.S. Navy in the 19th Century. For comparison, here are dimensions used by the U.S. Army, according to Edward S. Farrow, Farrow's Military Encyclopedia (New York: Edward S. Farrow, 1885):
Garrison flag - 20 feet hoist by 36 feet fly (1:1.8)Before anyone asks, the national standard for cavalry regiments was not the S&S, but a blue 2 ft 3 in by 2 ft 5 in flag with the U.S. COA. Cavalry regiments in 1885 carried only the one standard.
Post flag - 10 feet hoist by 20 feet fly (1:2)
Storm flag - 4 feet 2 inches hoist by 8 feet fly (1:1.92)
Infantry, Artillery, and Engineer national color: 6 feet hoist by 6 feet 6 inches fly (1:1.083333...)
Camp color: 18 inches hoist by 20 inches fly (1:1.111...)
The union (canton) in all of these was 7/13 of the hoist by 1/3 of the fly.